hey, I had this math question today in my math class:
ok, if F(x) = e ^ ((-X^2)/b)
find the inflection points in terms of b.
So I know you take the second derrivative and set it to 0, but other than that, I can’t do it:o
so if there’s anyone here who can help, please do!
sorry, but I already know that:o
you see, it needs to be in terms of b, meaning b isn’t the variable, but a number. However, this number is unknown… it could be 5, 7, pi, 2894584565, anything. therefore, basically, I need an equation that says b = ??? does anyone know how I should do that?
thanks:)
F(x) = e ^ ((-X^2)/b)
F(x)/dx = -2x/b * e ^ ((-X^2)/b)
F2(x)/dx2 = 4x^2/b^2 * e ^ ((-X^2)/b) - e ^ ((-X^2)/b) * 2/b [by product rule]
0 = 4x^2/b^2 * e ^ ((-X^2)/b) - e ^ ((-X^2)/b) * 2/b
4x^2/b^2 * e ^ ((-X^2)/b) = e ^ ((-X^2)/b) * 2/b
cancel out the e factors:
4x^2/b^2 = 2/b
4x^2/b = 2
4x^2 = 2b
x^2 = b/2
double prime of fx is 0 when x = ± squareroot(b/2)
the question doesn’t ask what b is, but what x is in terms of b. You’ll never find a numerical answer for b because it’s a parameter.
this stuff is so easy after vector calculus and linear algebra : ]
thanks! I think my problem was that I just didn’t use the chain rule in the beginning so I just “left out” part of it, therefore never getting a correct answer. oh well, thanks again!
And if you really want to make sure that it is an inflection point, look at the third prime, evaluated at sqrt(b/2) - a quick calculation shows that, if b != 0 (otherwise this wouldn’t make sense anyway…) => F’’’(x) != 0, therefore you have an inflection point.
Haha ya his wording confused me. I thought he wanted a partial derivative or something…
man this is simple, let me explain it in baby terms
F(x) = e ^ ((-X^2)/b)
if you have three bagels, and i take one away, how many do you have left?
2
then i cut the bagels in half and put cream cheese on them, how many do you have now?
14
if your friend comes over and eats one then how many do you have then?
13
f(x)= 13
duh!
next time just try using this bagel technique…your welcome!
Oh man, you forgot to factor in the lox! The lox is essential ! Must use the lox factor!
ok, wu-man’s description is easy to understand…
but what’s lox?
Heh…google is your friend.
Heh…google is your friend.
oh really?
Lox is noted for its importance in Ashkenazic Jewish cuisine. … Gravad lox is not smoked, but it can be served in a similar fashion. …
(found with google)
I don’t see how jewish cuisine is related to calculus
No wonder you couldn’t figure out how to do the problem.